I. Introduction.- 1.1. Brief History of Attempts to Detect Celestial ?-Rays < 50 MeV.- 1.2. Astrophysical Significance of ?-Ray Line Astronomy.- II. Mechanisms for ?-Ray Line and Continuum Production.- 2.1. Basic Mechanisms and Sources.- 2.2. Thermal Radiation Field.- 2.3. Particle-Field Interactions.- 2.3.1. Compton Effect.- 2.3.2. Magnetobremsstrahlung.- 2.3.3. Photomeson Production.- 2.4. Particle-Matter Interactions.- 2.4.1. Bremsstrahlung.- a. Non-Thermal Bremsstrahlung.- b. Thermal Bremsstrahlung.- 2.4.2. ?0 Production by (p-p) and (p-?) Interactions and (p-p?) Interactions: (?0 ? 2?).- a. (p-p) and (p-?) Interactions.- b. Matter-Antimatter (p-p?) Interactions.- 2.4.3. Nuclear Excitations.- a. Nuclear Excitation by Charged Particles: (p, p??), (?, ???), (p, ?), (?, ?), Spallation, and Fission.- b. Nuclear Excitation by Neutrons: (n, n??), (n, ?), and Activation.- c. Thermonuclear (Exoergic Reactions).- 2.4.4. Positron-Electron Annihilation.- a. Single Photon Annihilation.- b. Free Two and Three Photon Annihilation.- c. Bound State (Positronium) Annihilation.- 2.5. Special Effects.- 2.5.1. Doppler Shifts.- 2.5.2. Gravitational and Cosmological Red Shifts.- 2.5.3. Absorption of ?-Rays in Galactic and Metagalactic Space.- 2.6. Summary of ?-Ray Spectra.- III. Theoretical Estimates of ?-Ray Emission.- 3.1. Solar ?-Rays.- 3.1.1. Calculation of ?-Ray Yield.- 3.1.2. Positron and Neutron Production.- a. ?-Rays from Positrons and Neutrons.- 3.1.3. Excited Nuclear States.- a. The Flux Ratio ?(4.43) ?(2.22).- 3.1.4. ?0 ?-Rays.- 3.1.5. Solar Flare ?-Rays Continuum.- 3.2. Cosmic Sources (Point and Localized).- 3.2.1. Supernova Remnants and Supernovae.- a. ?-Rays from the R-Process.- b. ?-Rays from Si Burning in SN Shells.- c. Gum Nebula.- d. ?-Ray Sources (> 100 MeV).- e. Supernovae (Prompt Emission).- 3.2.2. Neutron Stars.- 3.2.3. Flare Stars.- 3.2.4. Galactic Core and Disk.- a. ?-Rays $$ \tilde > $$ 30 MeV.- b. 0.51 MeV Line Radiation.- c. ?-Ray Lines from Galactic Cosmic Rays.- 3.2.5. ?-Rays from Black Holes.- 3.2.6. Cosmic ?-Ray Bursts (Vela Class).- 3.3. Cosmic Diffuse Sources.- IV. Interaction of ?-Rays with Matter.- 4.1. ?-Ray Properties.- 4.2. Interaction Processes.- 4.2.1. Photoelectric Effect.- 4.2.2. The Compton Effect.- a. Polarized Incident Radiation.- b. Unpolarized Incident Radiation.- 4.2.3. Pair Production.- V. ?-Ray Flux Observations.- 5.1. Solar Observations.- 5.1.1. OSO-7 ?-Ray Observations in August 1972.- a. The August 4 event.- b. Time Profiles of the Positron Annihilation and Neutron Capture Lines — August 4 Event.- c. Preflare Upper Limits — August 4 Event.- d. Shape of the 0.5 MeV Line — August 4 Event.- e. ?-Ray Continuum — August 4 Event.- f. August 7 Event.- g. Conclusions Regarding Solar ?-Rays.- 5.2. Cosmic Observations (Point and Localized Sources).- 5.2.1. Supernovae and Supernova Remnants.- a. Supernova Remnants.- b. Supernovae.- 5.2.2. Galactic Disk and Center.- 5.2.3. Galactic Center ?-Ray lines.- 5.3. Diffuse ?-Ray Flux Observations (100 keV to 100 MeV).- 5.3.1. Observations (100 keV to 10 MeV).- 5.3.2. Observations (10 MeV to 100 MeV).- 5.4. Transient ?-Ray Bursts.- VI. Experimental Considerations for Nuclear ?-Ray Astronomy.- 6.1. Background Factors.- 6.1.1. Ambient Neutral Backgrounds.- a. The Diffuse ?-Ray Flux.- b. Atmospheric ?-Rays.- c. Intrinsic Activity.- d. Atmospheric Neutrons.- 6.1.2. Instrument Activation (Local Production).- 6.1.3. Satellite Orbits.- a. Intermediate Latitudes.- b. Polar Orbits.- 6.1.4. Space Probes.- 6.1.5. Observed Backgrounds in Specific Balloon Experiments.- a. Alkali Halide Spectrometers.- b. Solid State Detector Measurements.- c. Compton Telescope.- 6.2. Design Limitations.- 6.3. Current Detection Methods.- 6.3.1. Shielded Detectors.- a. HEAO-A Collimated X- and ?-Ray Spectrometer.- b. Collimator with Shutter-Occulter (Large ?-Ray Telescope).- c. Anti-Collimator Spectrometer.- d. HEAO-C Collimated Solid State Spectrometer.- 6.3.2. Compton Telescopes.- VII. Conclusions.- Notes Added in Proof.- Appendices.- A. Attenuation Coefficients for ?-Ray Interactions.- B. Conversion Factors for Energy Units.- References.